dorsal/arxiv
View SchemaLie-Poisson Deformation of the Poincar\'e Algebra
| Authors | A. Stern, I. Yakushin |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9505030 |
| URL | https://arxiv.org/abs/q-alg/9505030 |
| DOI | 10.1063/1.531498 |
Abstract
We find a one parameter family of quadratic Poisson structures on ${\bf R}^4\times SL(2,C)$ which satisfies the property {\it a)} that it is preserved under the Lie-Poisson action of the Lorentz group, as well as {\it b)} that it reduces to the standard Poincar\'e algebra for a particular limiting value of the parameter. (The Lie-Poisson transformations reduce to canonical ones in that limit, which we therefore refer to as the `canonical limit'.) Like with the Poincar\'e algebra, our deformed Poincar\'e algebra has two Casimir functions which we associate with `mass' and `spin'. We parametrize the symplectic leaves of ${\bf R}^4\times SL(2,C)$ with space-time coordinates, momenta and spin, thereby obtaining realizations of the deformed algebra for the cases of a spinless and a spinning particle. The formalism can be applied for finding a one parameter family of canonically inequivalent descriptions of the photon.
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"abstract": "We find a one parameter family of quadratic Poisson structures on ${\\bf\nR}^4\\times SL(2,C)$ which satisfies the property {\\it a)} that it is preserved\nunder the Lie-Poisson action of the Lorentz group, as well as {\\it b)} that it\nreduces to the standard Poincar\\\u0027e algebra for a particular limiting value of\nthe parameter. (The Lie-Poisson transformations reduce to canonical ones in\nthat limit, which we therefore refer to as the `canonical limit\u0027.) Like with\nthe Poincar\\\u0027e algebra, our deformed Poincar\\\u0027e algebra has two Casimir\nfunctions which we associate with `mass\u0027 and `spin\u0027. We parametrize the\nsymplectic leaves of ${\\bf R}^4\\times SL(2,C)$ with space-time coordinates,\nmomenta and spin, thereby obtaining realizations of the deformed algebra for\nthe cases of a spinless and a spinning particle. The formalism can be applied\nfor finding a one parameter family of canonically inequivalent descriptions of\nthe photon.",
"arxiv_id": "q-alg/9505030",
"authors": [
"A. Stern",
"I. Yakushin"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"doi": "10.1063/1.531498",
"title": "Lie-Poisson Deformation of the Poincar\\\u0027e Algebra",
"url": "https://arxiv.org/abs/q-alg/9505030"
},
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